There are measurement errors on the hologram plane due to sensor and position mismatches. These errors are amplified if one predicts the pressures close to the sources: backward prediction. The Pressure estimation errors depend on the following parameters: the measurement spacing on the hologram plane, the prediction spacing on the prediction plane, and the distance between the hologram and the prediction plane. However the effects of these on the pressure estimation error is only qualitatively described. The goal of this paper is to examine the effects of the parameters quantitatively.
This paper deals with the cases of which the measurement errors are distributed irregularly on the hologram plane. The sensor mismatch and inaccurate measurement location, position mismatch, are mainly addressed. In such cases, one can assume that the measurement is a sample of many measurement events, and the cause of the measurement error is the white noise on the hologram plane. Then the bias and random error are derived mathematically. To examine the results, computer simulation is carried out and it is found that the random error is important in the backward prediction. The relationship between the random error amplification ratio and the parameters mentioned above is examined quantitatively in terms of their energies.
